It follows a report that his Government is considering putting the UK on the road to closer ties with the European Union, which alarmed Brexiteers.
Both Downing Street and senior ministers have sought to play down the suggestion.
I voted for Brexit, I believe in Brexit and I know that Brexit can deliver, and is already delivering, enormous benefits and opportunities for the country
Speaking at the Confederation of British Industry (CBI) annual conference in Birmingham, Mr Sunak said he wished to be “unequivocal” that the UK “will not pursue any relationship with Europe that relies on alignment with EU laws” under his stewardship.
“I voted for Brexit, I believe in Brexit and I know that Brexit can deliver, and is already delivering, enormous benefits and opportunities for the country – migration being an immediate one where we have proper control of our borders and are able to have a conversation with the country about the type of migration that we want and need,” he said.
“We weren’t able to do that inside the European Union, at least now we are in control of it.
“When it comes to trade, it means that we can open up our country to the world’s fastest-growing markets.
“I’ve just got back from the G20 in Indonesia, we’re talking about signing CPTPP, where we’ve got some of the most exciting, fastest-growing economies in the world and we can become a part of that trading bloc, that’s a fantastic opportunity for the UK.”
He said the UK could also have “regulatory regimes that are fit for the future that ensure that this country can be leaders in those industries that are going to create the jobs and the growth of the future”.
Earlier, immigration minister Robert Jenrick said it “couldn’t be further from the truth” that the UK is looking at emulating the Swiss-EU relationship, and insisted the “fundamental tenets” of the Brexit deal signed by Boris Johnson would not be renegotiated.
The Sunday Times reported “senior government figures” were planning to put the UK on a path towards arrangements similar to Switzerland’s to ensure access to the EU’s single market.
The model would involve more liberal EU migration – although full free movement would not be on the table – and payments to the Brussels budget, the newspaper reported.
But on Monday morning Mr Jenrick said there is “no question whatsoever” of the UK reopening the deal with the EU.
“We have a settled position on our relationship with the European Union, that’s the deal that was struck in 2019 and 2020 – and that’s the one that we intend to stick to,” he told TalkTV.
“That sets out the fundamental position that we don’t want to see a return to free movement, we don’t want to have the jurisdiction of European judges in the UK, and we don’t want to be paying any money to the European Union.
“Of course there will be things on which we can improve our relationship – trade, security, migration are all key topics, and the Prime Minister wants to have the most productive relationship possible with our European friends and neighbours.
“But there’s no question whatsoever of us reopening the fundamental tenets of that deal.”
A Government spokesperson labelled the Sunday Times story “categorically untrue”.
They said: “This Government is focused on using our Brexit freedoms to create opportunities that drive growth and strengthen our economy.
“Brexit means we will never again have to accept a relationship with Europe that would see a return to freedom of movement, unnecessary payments to the European Union or jeopardise the full benefit of trade deals we are now able to strike around the world.”
Switzerland and the EU have a close economic relationship based on a series of bilateral agreements, giving the country direct access to parts of the EU’s internal market including the free movement of people.
The UK is locked in long-running talks with the EU over the Northern Ireland Protocol, a post-Brexit arrangement for the region designed to avoid a border on the island of Ireland.
Unionists have opposed the protocol as impeding trade between Northern Ireland and Great Britain, placing a border in the Irish Sea.
This has resulted in the collapse of the Stormont Assembly, with top civil servants left to run government departments.
However, there have been renewed hopes in recent weeks that a deal can be secured and the relationship improved between the UK and the EU after years of tensions.
A Swiss-style veterinary agreement has been one of the options mooted by some on the EU side as a solution to the protocol dispute.
Meanwhile, a UK-Switzerland agreement on services was extended for three years.
This means UK professionals can continue to travel and operate freely in Switzerland for up to 90 days a year without needing a permit.
International Trade Secretary Kemi Badenoch said: “The UK and Swiss economies are both services powerhouses and closely aligned.
“Today’s agreement is a win-win for both sides. From financial services in Edinburgh to cyber security in Wales, the deal ensures UK businesses capitalise on the huge opportunities on offer.”
The UK and Switzerland will launch negotiations next year on a new free-trade agreement.